McCain and Sen. Dan Coats (R-Ind.) were speaking about the National Security Agency's (NSA) phone "metadata" collection program when Paul tried to ask a question. Coats said he had not yielded the floor to Paul, effectively blocking the 2016 presidential candidate from speaking. Coats then yielded to McCain for a question, instead.

"The senator from Kentucky needs to learn the rules of the Senate," McCain said. "Maybe the senator from Kentucky should know the rules of the Senate."

McCain and Coats support extending provisions of the Patriot Act, including a section the NSA has used to authorize its "metadata" collection program. Paul, however, opposes both an extension as well as a House-passed reform bill that would require private companies to hold the records.

He is threatening to use procedural tactics to draw out the fight over the program past midnight Sunday, which would force the program to expire.

The verbal battle came as senators debated what to do about the provisions, with debate time equally divided between Republicans and Democrats. Coats and McCain used up the Republican debate time, and when Paul requested to use five minutes from the Democratic side, McCain objected.

Speaking to a staffer on the Senate floor, the Kentucky Republican said that "I sat here and watched the clock for 30 minutes. It was not equally divided time."

Paul also tried to use a procedural tactic to overturn McCain's objection, but failed to get another senator to support his request.

The Kentucky Republican was eventually allowed to speak from the Senate floor about the NSA program.

"I'm not going to take it anymore," he said, referring to the NSA program. "I don't think the American people are going to take it anymore."

Paul has been caught in a battle with Majority Leader Mitch McConnell (R-Ky.) over how to proceed on the Patriot Act.

But Paul on Sunday blamed President Obama, not McConnell, saying "let's be very clear why we're here. President Obama set this program up."